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Topology of high-dimensional chaotic scattering
1Department of Mathematics, Department of Electrical Engineering, and Department of Physics, Center for Systems Science and Engineering Research, Arizona State University, Tempe, Arizona 85287-1804, USA.
Summary
We discovered a topological metamorphosis in Hamiltonian chaotic scattering within 3D potentials. This change, driven by system parameters like energy, alters the scattering basin
Area of Science:
- Physics
- Classical Mechanics
- Chaos Theory
Background:
- Hamiltonian chaotic scattering describes complex particle trajectories.
- Understanding basin topology is crucial for predicting scattering outcomes.
Purpose of the Study:
- Investigate topological changes in scattering basin dynamics.
- Explain the origin of these topological metamorphoses.
- Analyze consequences for chaotic scattering.
Main Methods:
- Simulations of Hamiltonian chaotic scattering in 3D potentials.
- Analysis of invariant sets of non-escaping orbits.
- Calculation of fractal dimensions of chaotic sets.
Main Results:
- A topological metamorphosis of the scattering basin was observed.
- This metamorphosis occurs as a system parameter (e.g., energy) crosses a critical value.
- The change is linked to alterations in the invariant set structure.
- Fractal dimensions of chaotic sets exhibit characteristic changes at metamorphosis.
Conclusions:
- The study reveals a novel topological metamorphosis in 3D Hamiltonian chaotic scattering.
- This phenomenon is driven by changes in the invariant set of non-escaping orbits.
- The observed metamorphosis has no parallel in 2D systems.
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